\documentclass[12pt,a4paper]{article}

\include{preamble}

\begin{document}

\maketitle

\section*{第一题} 

\begin{figure}[htbp] 
	\centering
	\includegraphics[width=12cm]{bayers_01.png}
\end{figure} 

\begin{enumerate}

\item 绘制系统的信息矩阵 $\Lambda$

\begin{figure}[!h]
  \centering
  \input{tikz_ifm.tex}
\end{figure}

\newpage

\item 绘制相机$\xi_1$被marg以后的信息矩阵 $\Lambda^{\prime}$

\begin{figure}[!h]
  \centering
  \input{tikz_ifm_marg.tex}
\end{figure}

\end{enumerate}


\section*{第二题}

\noindent
\setlength{\parindent}{2em}
\setlength{\parskip}{0.3em}

$$
\boldsymbol{\Lambda} = 
\begin{bmatrix}
\mathbf{J_T}^T \\ \mathbf{J_P}^T
\end{bmatrix}
\begin{bmatrix}
\mathbf{J_T} & \mathbf{J_P}
\end{bmatrix} = 
\begin{bmatrix}
\mathbf{J_T}^T \mathbf{J_T} & \mathbf{J_T}^T \mathbf{J_P} \\
\mathbf{J_P}^T \mathbf{J_T} & \mathbf{J_P}^T \mathbf{J_P}
\end{bmatrix}
$$

单目Bundle Adjustment信息矩阵中补充的代码如下：

\begin{lstlisting}
H.block(j*3+6*poseNums,j*3+6*poseNums,3,3) += jacobian_Pj.transpose() * jacobian_Pj;
H.block(i*6,j*3+6*poseNums,6,3) += jacobian_Ti.transpose() * jacobian_Pj;
\end{lstlisting}

输出结果（奇异值）的最后7维如下：

\begin{lstlisting}
1.25708e-16
8.63763e-17
5.18689e-17
4.38809e-17
2.98776e-17
1.45304e-17
1.59456e-18
\end{lstlisting}

奇异值的最后7维接近0，表明零空间的维度为7。

\bibliographystyle{unsrt}
\bibliography{bibfile}

\end{document}

